How collaborative filtering recommends from ratings alone

Here is the thing that still feels a little magical to me about recommender systems: a good one can suggest a film in a genre you have never touched, and be right, without knowing a single thing about what the film is actually about. No plot summary, no cast list, no tags. It works purely from the pattern of who rated what. That is collaborative filtering, and once it clicks it is surprisingly simple. The starting point is a big table. Rows are users, columns are items, and each cell holds a…